"You play it your way; I play it Bach's way." Addressing the indomitable harpsichordist Wanda Landowska, the equally indomitable Rosalyn Tureck, who has died aged 88, made one of her most famous and characteristic statements. For JS Bach was the composer to whom this strong-willed, demanding and fearsomely intelligent American keyboard player dedicated her life, both as performer and scholar.

She was born in Chicago, the granddaughter of a famous Kiev cantor; she related, with great pride, her father's tales of a carriage, pulled by eight white horses, taking her grandfather on tour for the high holy days. Her main teachers were Sophia Brilliant-Liven, Jan Chiapusso and Olga Samaroff (the American wife of conductor Leopold Stokowski) and, for harpsichord, Gavin Williamson.

Her talent showed itself early, and she made her public recital debut in Chicago at the age of nine. When, at 16, she auditioned for the Juilliard School of Music, New York, she startled the panel by offering to play most of Bach's 48 preludes and fugues from memory.

Shortly afterwards, she settled on her future direction during a strange episode in a Juilliard practice room. While working on a Bach fugue, she blacked out for a short time; she came round with an inner revelation that she needed to create a different type of keyboard technique specific to the playing of Bach. Her teacher told her it was a wonderful, but impossible, idea; in response, she changed teachers. She never stopped perfecting this apparently elusive notion.

But Tureck's dedication was not only to Bach. At the age of 10, she had met the Russian musical inventor Leon Theremin, and heard the electronic instrument known by his surname; the experience made a huge impression on her. During her first week at the Juilliard, she learnt of a year-long scholarship available to a would-be student of the theremin; she promptly auditioned - working out God Save The Queen on the instrument, which she had never played before - and duly won the award.

Her 1932 debut at Carnegie Hall was made on the theremin, rather than the piano. She always continued to champion electronic instruments by such innovators as Robert Moog, who gave her one of his synthesizers, and Henry Beniof, with whom she worked for 20 years on the development of an electronic piano.

Tureck made her New York piano recital debut in 1935, and, in the same year, gave her first all-Bach series there; later, she would give annual all-Bach series in New York (from 1944 to 1954, and from 1959 to the 1980s), in London (from 1953), in Copenhagen (from 1956) and in Pasadena (through the 1960s and 70s). At 22, she made her orchestral debut in New York with the Philadelphia Orchestra, under the baton of Eugene Ormandy at Carnegie Hall, playing Brahms's gigantic Second Piano Concerto - nothing daunted by her own slight build (she was 5ft 2in tall) and tiny, if extremely flexible, hands.

Tureck's early career had all the trappings of conventional stardom. She toured the US constantly, performing the great pianistic war-horse concertos - she spoke affectionately of travelling with the Minneapolis Symphony Orchestra and Dimitri Mitropoulos, in a private train while still 22, and playing the Rachmaninov Second Concerto every night in a different town.

Recordings from the early 1940s demonstrate that she was not only a fastidious performer of Bach but also an exceptional virtuoso - a recording re-released on the VAI label, under the title The Young Firebrand, includes a breathtaking performance of Liszt's Paganini Etudes.

Tureck, likewise, championed contemporary music, especially that of American composers such as Charles Ives, William Schuman and David Diamond; Diamond's First Piano Sonata of 1947 was written for her, and she premiered Schuman's Piano Concerto. Her own interest in composition had stretched to some lessons with Arnold Schoenberg, and, in 1952, she presented the first programme in the United States of tape and electronic music.

Such a career would satisfy many musicians, but not Tureck. After her international reputation was established with her European debut in Copenhagen in 1947 and her London debut - three Bach recitals - in 1953, she expanded her remit still further. She founded her own orchestra, the Tureck Bach Players, which existed from 1960 to 1972, and she became the first woman to conduct the New York Philharmonic in a subscription concert (1958) and the Philharmonia Orchestra in London (1959).

She held teaching posts and professorships widely, teaching first at the Philadelphia Conservatory (1935-42), the Mannes School of Music in New York (1940-44), Juillard (1943-55) and Columbia University, New York (1953-55); she was also professor of music at the University of Maryland from 1982 to 1984. In 1970, she was made a life fellow of St Hilda's College, Oxford, and three years later became a visiting fellow of Wolfson College, Oxford.

In the intervening years, she made appearances lecturing at educational establishments from Denmark, Spain and Holland to Israel, Brazil, Chile and Argentina, as well as the US.

Her books included Introduction To The Performance Of Bach, in three volumes (OUP, 1960), and she worked on editions of several of Bach's works, including the Italian Concerto (1983) and two of the lute suites, with the guitarist Sharon Isbin.

"The whole tenor of my life has been bringing what seem to be opposing worlds and areas together," she told me in 1993; and to this end, she founded several musical and research societies: Composers of Today, New York City, 1949-53; the International Bach Society in 1966, and the Institute for Bach Studies, New York, two years later; the Tureck Bach Institute, New York, 1966-90; and last but not least, the Tureck Bach Research Foundation (TBRF) of Oxford in 1993.

The TBRF held an annual symposium at which distinguished speakers from different disciplines - ranging from music to astrophysics and Egyptology - addressed the same topic, such as structure or embellishment. At those meetings, Tureck played Bach on everything from the harpsichord to the Steinway and the synthesizer - often on several instruments during one concert - and she had little patience for the restrictive attitudes that declared Bach should only be played on historical instruments.

Thus, the 1997 symposium did much to challenge the concept of historically aware authenticity that had dominated the musical world through the previous quarter century, with speakers from various disciplines maintaining that it was fundamentally flawed.

Tureck was a formidable personality, who demanded immensely high standards of herself and others, but she also possessed a great deal of charm, and an intellect that was as lively as ever in her mid-80s (when I once encountered her wearing leather from head to foot). In 1964, at the age of 50, she married an American architect, George Wallingford Downs, who tragically died the same year; she did not marry again.

In the early 1990s, she moved to Oxford, where she subsequently devoted much of her time to the TBRF. She continued to perform widely, appearing in St Petersburg, Italy, New York and at the Wigmore Hall, London; in 1998, she also made a new piano recording, for Deutsche Grammophon, of the work perhaps most strongly associated with her, Bach's Goldberg Variations, which she had sometimes played twice over in concerts - first on the harpsichord, then on the piano. Her earlier recordings, still available on Philips, VAI and other labels, are historic classics. Last year, she returned to New York.

Tureck's pianistic style, which (unfairly enough) was a huge influence on the more celebrated Glenn Gould, was uncompromisingly rigorous, intelligent and full of attention to detail: she took, for example, great care over the appropriateness of ornamentation. But what always convinces the listener is the compelling, incandescent, almost evangelical spirit that shines through that detail. She was hailed as "the high priestess of Bach" - and that is how she will be remembered.